Find all k-sized subsets of arbitrary integer set such that xor is 0

why.jl

function set_xor(set::Set{T}) where T 
		
	res = undef
	front::Bool = true
	for e in set
		if front 
			res = e
			front = false
		else
			res = Base.xor(res, e)
		end
	end
	return res
end

function solve(set_in::Set, k::Integer) ::Set{Set}

	pool = Vector{Set{Set}}()
	push!(pool, Set())

	# seed the pool with all sets of size 1
	for n in set_in
		push!(pool[1], Set([n]))
	end
	
	# grow sets to generate all possible sets of size k-1
	index = 2
	while index <= k-1

		push!(pool, Set{Set}())
		for set in pool[index-1]
			for n in set_in
				push!(pool[index], union(set, Set([n])))
			end
		end
		index += 1
	end

	# reject some k-1 because: 
	# For a set s = {s1, s2, ..., s3} such that xor(s) != 0, m = xor(s): xor(union(s, m)) = 0
	out = Set{Set}()
	for set in pool[length(pool)]

		xor_result = set_xor(set)
		if !(xor_result in set) && (xor_result in set_in)
			push!(out, union(set, Set([xor_result])))
		end 
	end

	return out
end

# usage:
solve(Set([x for x in 1:256]), 5)